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Definition: The F-Distribution is also called as Variance Ratio Distribution as it usually defines the ratio of the variances of the two normally distributed populations. The F-distribution got its name after the name of R.A. Fisher, who studied this test for the first time in 1924. Symbolically, the quantity is distributed as F-distribution with ν1 =n1-1 and ν2 = n2-1 … [Read more...] about F-Distribution

Definition: The t-distribution is a probability distribution method wherein the hypothesis of the mean of a small sample is tested, which is drawn from the systematic population whose standard deviation is unknown. It is a statistical measure used to compare the observed data with the data expected to be obtained from a specific hypothesis. Applications of t-distribution The … [Read more...] about Applications of t-Distribution

Definition: The t-Distribution, also known as Student’s t-Distribution is the probability distribution that estimates the population parameters when the sample size is small and the population standard deviation is unknown. It resembles the normal distribution and as the sample size increases the t-distribution looks more normally distributed with the values of means and … [Read more...] about t-Distribution

Definition: The Degrees of Freedom refers to the number of values involved in the calculations that have the freedom to vary. In other words, the degrees of freedom, in general, can be defined as the total number of observations minus the number of independent constraints imposed on the observations. The degrees of freedom are calculated for the following statistical tests … [Read more...] about Degrees of Freedom

Definition: The Hypothesis is an assumption which is tested to check whether the inference drawn from the sample of data stand true for the entire population or not. Hypothesis Testing Procedure The following steps are followed in hypothesis testing: Set up a Hypothesis: The first step is to establish the hypothesis to be tested. The statistical hypothesis is an … [Read more...] about Hypothesis Testing Procedure

Definition: The Hypothesis Testing is a statistical test used to determine whether the hypothesis assumed for the sample of data stands true for the entire population or not. Simply, the hypothesis is an assumption which is tested to determine the relationship between two data sets. In hypothesis testing, two opposing hypotheses about a population are formed Viz. Null … [Read more...] about Hypothesis Testing

Definition: The Sampling Distribution of Standard Deviation estimates the standard deviation of the samples that approximates closely to the population standard deviation, in case the population standard deviation is not easily known. Thus, the sample standard deviation (S) can be used in the place of population standard deviation (σ). Symbolically, S= standard error of the … [Read more...] about Sampling Distribution of Standard Deviation

Definition: The Sampling Distribution of Proportion measures the proportion of success, i.e. a chance of occurrence of certain events, by dividing the number of successes i.e. chances by the sample size ’n’. Thus, the sample proportion is defined as p = x/n. The sampling distribution of proportion obeys the binomial probability law if the random sample of ‘n’ is obtained … [Read more...] about Sampling Distribution of Proportion

Definition: The Sampling Distribution of the Difference between Two Means shows the distribution of means of two samples drawn from the two independent populations, such that the difference between the population means can possibly be evaluated by the difference between the sample means. Let say, there are two populations, first of size N1, with mean ?1, and standard … [Read more...] about Sampling Distribution of the Difference Between Two Means

Definition: The Sampling Distribution of Median shows the distribution of sample medians, a mid-value in the items arranged in some chronological order in the sample drawn from the population. If the population is large approximated by the normal distribution with mean? And a standard deviation σ, the medians of random samples of size n are distributed with mean? And a … [Read more...] about Sampling Distribution of Median